Foreman-Mackey (Flatiron) showed me something interesting today: He is doing full sampling of one-planet and two-planet transiting systems in Kepler but using models that have many more than one or two planets. Where many is like four! But he is learning some very interesting things: One is that you can do this, as long as you let planet radii go to zero. Another is that the ease of sampling depends strongly on the eccentricity prior. That isn't surprising in retrospect.
One of the motivations of this, I think, is to get away from computing Bayesian evidence between different multiplicity models: After all, to compute these ratios, you have to sample a large N, so why not just do that one N once and treat the problem as a parameter-estimation problem, rather than an evidence problem? That's dear to my heart. Another angle that I'm interested in is the following: We know that our own Solar System in fact has thousands to millions of planets; can we deal with it in a more non-parametric way?
Crazy idea: Send N to infinity and fix the planet periods (say) and then see if you can sample in the other orbital parameters. Right now that doesn't seem feasible, but it might be the truly non-parametric approach.